Chapter 5: Q. 111 (page 521)

(a) $a^{3} . a^{- 3}$
(b) $(u v^{- 2}) (u^{- 5} v^{- 3})$
(c) $(- 4 r^{- 2} s^{- 8}) (9 r^{4} s^{3})$

Short Answer

Expert verified

(a) $1$

(b) $u^{- 4} v^{- 5}$

Step by step solution

Part (a) Step 1 . Given Information

We are given the expression :

$a^{3} . a^{- 3}$ , we need to simplify the expression

Part (a) Step 2 . Product Property and Zero Exponent Property

If $a$ is a real number and $m$ and $n$ are integers, then :

$a^{m} . a^{n} = a^{m + n}$

$a^{0} = 1$

Part (a) Step 3 . Simplify the expression

Using the Product Property :

$a^{3} . a^{- 3} = a^{3 + (- 3)}$

$a^{3 - 3} = a^{0}$

$a^{0} = 1$ (zero exponent property)

Part (b) Step 1 . Given Information

We are given the expression :

$(u v^{- 2}) (u^{- 5} v^{- 3})$ , we need to simplify the expression

Part (b) Step 2 . Product Property

If $a$ is a real number and $m$ and $n$ are integers, then :

$a^{m} . a^{n} = a^{m + n}$

Part (b) Step 3 . Simplify the expression

Using the Product Property :

$(u v^{- 2}) (u^{- 5} v^{- 3}) = u^{1 + (- 5)} v^{- 2 + (- 3)}$

$u^{1 - 5} v^{- 2 - 3} = u^{- 4} v^{- 5}$

Part (c) Step 1 . Given Information

We are given the expression :

$(- 4 r^{- 2} s^{- 8}) (9 r^{4} s^{3})$ , we need to simplify the expression

Part (c) Step 2 . Product Property

If $a$ is a real number and $m$ and $n$ are integers, then :

$a^{m} . a^{n} = a^{m + n}$

Part (c) Step 3 . Simplify the expression

Using the Product Property :

$(- 4 r^{- 2} s^{- 8}) (9 r^{4} s^{3}) = (- 4.9 r^{- 2 + 4}) (s^{- 8 + 3})$

role="math" localid="1644991761380" $= - 36 r^{2} s^{- 5}$

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(a) $a^{3} . a^{- 3}$
(b) $(u v^{- 2}) (u^{- 5} v^{- 3})$
(c) $(- 4 r^{- 2} s^{- 8}) (9 r^{4} s^{3})$

Short Answer

Step by step solution

Part (a) Step 1 . Given Information

Part (a) Step 2 . Product Property and Zero Exponent Property

Part (a) Step 3 . Simplify the expression

Part (b) Step 1 . Given Information

Part (b) Step 2 . Product Property

Part (b) Step 3 . Simplify the expression

Part (c) Step 1 . Given Information

Part (c) Step 2 . Product Property

Part (c) Step 3 . Simplify the expression

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(a)a3.a-3(b)(uv-2)(u-5v-3)(c)(-4r-2s-8)(9r4s3)

Short Answer

Step by step solution

Part (a) Step 1 . Given Information

Part (a) Step 2 . Product Property and Zero Exponent Property

Part (a) Step 3 . Simplify the expression

Part (b) Step 1 . Given Information

Part (b) Step 2 . Product Property

Part (b) Step 3 . Simplify the expression

Part (c) Step 1 . Given Information

Part (c) Step 2 . Product Property

Part (c) Step 3 . Simplify the expression

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

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Statistics

Pure Maths

Study anywhere. Anytime. Across all devices.

(a) $a^{3} . a^{- 3}$
(b) $(u v^{- 2}) (u^{- 5} v^{- 3})$
(c) $(- 4 r^{- 2} s^{- 8}) (9 r^{4} s^{3})$