Chapter 8: Q. 8.66 (page 782)

Simplify:
a. $y^{\frac{3}{4}} \cdot y^{\frac{5}{8}}$ b. ${(m^{9})}^{\frac{2}{9}}$ c. $\frac{d^{\frac{1}{5}}}{d^{\frac{6}{5}}}$

Short Answer

Expert verified

Part (a). The answer is $y^{\frac{11}{8}}$ .

Part (b). The answer is $m$ .

Part (c). The answer is $\frac{1}{d}$

Step by step solution

Part (a) Step 1. Simplifying

We know that if the base of the exponent is the same in the multiplication then we have to add the powers.

So,

$= y^{\frac{3}{4}} \cdot y^{\frac{5}{8}} = y^{\frac{3}{4} + \frac{5}{8}} = y^{\frac{6 + 5}{8}} = y^{\frac{11}{8}}$

Part (b) Step 1. Simplifying the exponent

We know that, ${(a^{b})}^{c} = a^{b \cdot c}$

Similarly,

${(m^{9})}^{\frac{2}{9}} m^{9 \times \frac{2}{9}} m$

Step 3 / 3Part (c) Step 1. Simplifying the exponent

We know that, $\frac{a^{b}}{a^{c}} = a^{b - c}$

Similarly,

$\frac{d^{\frac{1}{5}}}{d^{\frac{6}{5}}} d^{\frac{1}{5} - \frac{6}{5}} d^{\frac{1 - 6}{5}} d^{\frac{- 5}{5}} d^{- 1} \frac{1}{d}$

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Simplify:
a. $y^{\frac{3}{4}} \cdot y^{\frac{5}{8}}$ b. ${(m^{9})}^{\frac{2}{9}}$ c. $\frac{d^{\frac{1}{5}}}{d^{\frac{6}{5}}}$

Short Answer

Step by step solution

Part (a) Step 1. Simplifying

Part (b) Step 1. Simplifying the exponent

Step 3 / 3Part (c) Step 1. Simplifying the exponent

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Simplify:a.y34·y58b.m929c.d15d65

Short Answer

Step by step solution

Part (a) Step 1. Simplifying

Part (b) Step 1. Simplifying the exponent

Step 3 / 3Part (c) Step 1. Simplifying the exponent

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Decision Maths

Statistics

Theoretical and Mathematical Physics

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Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Simplify:
a. $y^{\frac{3}{4}} \cdot y^{\frac{5}{8}}$ b. ${(m^{9})}^{\frac{2}{9}}$ c. $\frac{d^{\frac{1}{5}}}{d^{\frac{6}{5}}}$