Q. 82.

Question

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

$ⓐ x^{4} \cdot x^{2} ⓑ 8^{9 x} \cdot 8^{3} ⓒ 3 z^{25} \cdot 5 z^{8} ⓓ y \cdot y^{3} \cdot y^{5}$

Step-by-Step Solution

Verified

Answer

The simplified form of given expression $x^{4} \cdot x^{2} = x^{6}$

The simplified form of given expression $8^{9 x} \cdot 8^{3} = 8^{9 x + 3}$

The simplified form of given expression $3 z^{25} \cdot 5 z^{8} = 15 z^{33}$

The simplified form of given expression $y \cdot y^{3} \cdot y^{5} = y^{9}$

1Step 1. Given Information

In the given question we have to simplify the given expression:
$ⓐ x^{4} \cdot x^{2} ⓑ 8^{9 x} \cdot 8^{3} ⓒ 3 z^{25} \cdot 5 z^{8} ⓓ y \cdot y^{3} \cdot y^{5}$

2Part (a) Step 1. The given expression is x 4 · x 2

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

$x^{4} \cdot x^{2} = x^{4 + 2}$

Simplify.

$x^{4} \cdot x^{2} = x^{6}$

3Part (b) Step 1. The given expression is 8 9 x · 8 3

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

$8^{9 x} \cdot 8^{3} = 8^{9 x + 3}$

4Part (c) Step 1. The given expression is 3 z 25 · 5 z 8

$3 z^{25} \cdot 5 z^{8} = 3 \cdot 5 \cdot z^{25} \cdot z^{8}$

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

$3 z^{25} \cdot 5 z^{8} = 15 \cdot z^{25 + 8}$

Simplify.

$3 z^{25} \cdot 5 z^{8} = 15 z^{33}$

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

$y \cdot y^{3} \cdot y^{5} = y^{1} \cdot y^{3} \cdot y^{5}$

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

$y \cdot y^{3} \cdot y^{5} = y^{1 + 3 + 5}$

Simplify.

$y \cdot y^{3} \cdot y^{5} = y^{9}$

Q. 81

Q. 83.

Other exercises in this chapter

Q. 5.48

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

In the following exercises, simplify each expression using the properties for exponents.mx·m3

View solution