Q. 81

Question

In the following exercises, simplify each expression using the properties for exponents.

$ⓐ d^{3} \cdot d^{6} ⓑ 4^{5 x} \cdot 4^{9 x} ⓒ 2 y \cdot 4 y^{3} ⓓ w \cdot w^{2} \cdot w^{3}$

Step-by-Step Solution

Verified

Answer

The simplified form of given expression $d^{3} \cdot d^{6} = d^{9}$

The simplified form of given expression $4^{5 x} \cdot 4^{9 x} = 4^{14 x}$

The simplified form of given expression $2 y \cdot 4 y^{3} = 8 y^{4}$

The simplified form of given expression $w \cdot w^{2} \cdot w^{3} = w^{6}$

1Step 1. Given Information

In the given question we have to simplify the given expression:

$ⓐ d^{3} \cdot d^{6} ⓑ 4^{5 x} \cdot 4^{9 x} ⓒ 2 y \cdot 4 y^{3} ⓓ w \cdot w^{2} \cdot w^{3}$

2Part (a) Step 1. The given expression is d 3 · d 6

Use the Product Property, $a^{m} \cdot a^{n} = a^{m + n}$

$d^{3} \cdot d^{6} = d^{6 + 3}$

Simplify.

$d^{3} \cdot d^{6} = d^{9}$

3Part (b) Step 1. The given expression is 4 5 x · 4 9 x

Use the Product Property, $a^{m} \cdot a^{n} = a^{m + n}$

$4^{5 x} \cdot 4^{9 x} = 4^{5 x + 9 x}$

Simplify.

$4^{5 x} \cdot 4^{9 x} = 4^{14 x}$

4Part (c) Step 1. The given expression is 2 y · 4 y 3

$2 y \cdot 4 y^{3} = 2 y^{1} \cdot 4 y^{3}$

$2 y \cdot 4 y^{3} = 2 \cdot 4 \cdot y^{1} \cdot y^{3}$

Use the Product Property, $a^{m} \cdot a^{n} = a^{m + n}$

$2 y \cdot 4 y^{3} = 2 \cdot 4 \cdot y^{3 + 1}$

Simplify.

$2 y \cdot 4 y^{3} = 8 y^{4}$

5Part (d) Step 1. The given expression is   w · w 2 · w 3

$w \cdot w^{2} \cdot w^{3} = w^{1} \cdot w^{2} \cdot w^{3}$

Use the Product Property, $a^{m} \cdot a^{n} = a^{m + n}$

$w \cdot w^{2} \cdot w^{3} = w^{1 + 2 + 3}$

Simplify.

$w \cdot w^{2} \cdot w^{3} = w^{6}$

Q. 5.48

Q. 82.

Other exercises in this chapter

Q. 5.47

Multiply or divide as indicated. Write answers in decimal form:ⓐ (−3×105)(2×10−8) ⓑ 8×1024×10−2

View solution

Q. 5.48

Multiply or divide as indicated. Write answers in decimal form:ⓐ (−3×10−2)(3×10−1) ⓑ 8×1042×10&