# Class 8 RD Sharma Solutions – Chapter 6 Algebraic Expressions And Identities – Exercise 6.3 | Set 1

**Find each of the following products:**

**Question 1: **5x^{2} * 4x^{3}

**Solution: **

First, separate the numbers and variables.

= (5 * 4) * (x

^{2}* x^{3})Add the powers of the same variable and multiply the numbers.

= 20 * (x

^{2+3})= 20x

^{5}

**Question 2: **-3a^{2} * 4b^{4}

**Solution: **

First, separate the numbers and variables.

= (-3 * 4) * (a

^{2}) * (b^{4})= -12a

^{2}b^{4}

**Question 3: **(-5xy) * (-3x^{2}yz)

**Solution: **

First separate the numbers and variables.

= (-5 * -3) * (x * x

^{2}) * (y * y) * (z)Add the powers of the same variable and multiply the numbers.

= 15 * (x

^{1+2}) * (y^{1+1}) * (z)= 15x

^{3}y^{2}z

**Question 4: **(1/2)xy * (2/3)x^{2}yz^{2}

**Solution: **

First separate the numbers and variables.

= ((1/2) * (2/3)) * (x * x

^{2}) * (y * y) * (z^{2})Add the powers of the same variable and multiply the numbers.

= (1/3) * (x

^{1+2}) * (y^{1+1}) * (z^{2})= (1/3)x

^{3}y^{2}z^{2}

**Question 5: **((-7/5)xy^{2}z) * ((13/3)x^{2}yz^{2})

**Solution: **

First separate the numbers and variables.

= ((-7/5) * (13/3)) * (x * x

^{2}) * (y^{2}* y) * (z * z^{2})Add the powers of the same variable and multiply the numbers.

= (-91/15) * (x

^{1+2}) * (y^{2 +1})^{ * }(z^{1+2})= (-91/15)x

^{3}y^{3}z^{3}

**Question 6:**^{ }(( -24/25 )x^{3}z) * ((-15/16 )xz^{2}y)

^{ }

**Solution: **

First separate the numbers and variables.

= ((-24/25) * (-15/16)) * (x

^{3}* x) * (z * z^{2}) * (y)Add the powers of the same variable and multiply the numbers.

= (9/4) * (x

^{3+1}) * (z^{1+2}) * (y)= (9/10)x

^{4}yz^{3}

**Question 7: **((-1/27)a^{2}b^{2}) * ((9/2))a^{3}b^{2}c^{2})

**Solution: **

First separate the numbers and variables.

= ((-1/27)) * (9/2)) * (a

^{2 }* a^{3}) * (b^{2 }*^{ }b^{2}) * (c^{2})Add the powers of the same variable and multiply the numbers.

= (-1/6) * (a

^{2+3}) * (b^{2+2}) * (c^{2})= (-1/6)a

^{5}b^{4}c^{2}

**Question 8: **(-7xy) * ((1/4)x^{2}yz)

**Solution: **

First separate the numbers and variables.

= (-7 * (1/4)) * (x * x

^{2}) * (y * y) * (z)Add the powers of the same variable and multiply the numbers.

= (-7 * (1/4)) * (x

^{1+2}) * (y^{1+1}) * (z)= (-7/4) x

^{3}y^{2}z

**Question 9: **(7ab) * (-5ab^{2}c) * (6abc^{2})

**Solution: **

First separate the numbers and variables.

= (7 * -5 * 6) * (a * a * a) * (b * b

^{2 }* b) * (c * c^{2})Add the powers of the same variable and multiply the numbers.

= -210 * (a

^{1+1+1}) * (b^{1+2+1}) * (c^{1+2})= -210a

^{3}b^{4}c^{3}

**Question 10: **(-5a) * (-10a^{2}) * (-2a^{3})

**Solution: **

First separate the numbers and variables.

= (-5 * -10 * -2) * (a * a

^{2 }* a^{3})Add the powers of the same variable and multiply the numbers.

= (-100) * (a

^{1+2+3})= -100a

^{6}

**Question 11:** (-4x^{2}) * (-6xy^{2}) * (3yz^{2})

**Solution:**

First separate the numbers and variables.

= (-4 * -6 * 3) * (x

^{2}* x) * (y^{2}* y) * (z^{2})Add the powers of the same variable and multiply the numbers.

= -72 * (x

^{2+1}) * (y^{2+1}) * (z^{2})= -72x

^{3}y^{3}z^{2}

**Question 12:** ((-2/7 )a^{4}) * ((-3/4 )a^{2}b) * ((-14/5 )b^{2})

**Solution:**

First separate the numbers and variables.

= ((-2/7) * (-3/4) * (-14/5)) * (a

^{4}* a^{2}) * (b * b^{2})Add the powers of the same variable and multiply the numbers.

= (-3/5) * (a

^{4+2}) * (b^{1+2})= (-3/5)a

^{6}b^{3}

**Question 13:** ((7/9)ab^{2}) * ((15/7) ac^{2}b) * ((-3/5)a^{2}c)

**Solution: **

First separate the numbers and variables.

= ((7/9) * (15/7) * (-3/5)) * (a * a * a

^{2}) * (b^{2}* b) * (c^{2}* c)Add the powers of the same variable and multiply the numbers.

= (-1) * (a

^{1+1+2}) * (b^{2+1}) * (c^{2+1})= -a

^{4}b^{3}c^{3}

**Question 14:** ((4/3)u^{2}vw) * (-5uvw^{2}) * ((1/3)v^{2}wu)

**Solution: **

First separate the numbers and variables.

= ((4/3) * (-5) * (1/3)) * (u

^{2}* u * u) * (v * v * v^{2}) * (w * w^{2}* w)Add the powers of the same variable and multiply the numbers.

= (-20/9) * (u

^{2+1+1}) * (v^{1+1+2}) * (w^{1+2+1})= (-20/9)u

^{4}v^{4}w^{4}

**Question 15:** (0.5x) * ((1/3) xy^{2}z^{4}) * (24x^{2}yz)

**Solution:**

First separate the numbers and variables.

= ((0.5) * (1/3) * (24)) * (x * x * x

^{2}) * (y^{2}* y) * (z^{4}* z)Add the powers of the same variable and multiply the numbers.

= (4) * (x

^{1+1+2}) * (y^{2+1}) * (z^{4+1})= 4x

^{4}y^{3}z^{5}

**Question 16:** ((4/3)pq^{2}) * ((-1/4)p^{2}r) * (16p^{2}q^{2}r^{2})

**Solution:**

First separate the numbers and variables.

= (( 4/3) * (-1/4) * (16)) * (p * p

^{2}* p^{2}) * (q^{2}* q^{2}) * (r * r^{2})Add the powers of the same variable and multiply the numbers.

= (-16/3) * (p

^{1+2+2}) * (q^{2+2}) * (r^{1+2})= (-16/3)p

^{5}q^{4}r^{3}

**Question 17:** (2.3xy ) * ( 0.1x ) * ( 0.16 )

**Solution: **

First separate the numbers and variables.

= (2.3 * 0.1 * 0.16) * (x * x) * (y)

Add the powers of the same variable and multiply the numbers.

= 0.0368 * (x

^{1+1}) * (y)= 0.0368x

^{2}y

### Chapter 6 Algebraic Expressions and Identities – Exercise 6.3 | Set 2

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