Exponential functions

Exponential functions > Exponents and powers

Overview

12345Exponents and powers

Exercises

Exercise 1

Compute:

$\frac{17^{105}}{17^{23}} \cdot 17^{-85}$

${(\frac{1}{2})}^{219} \cdot 8^{72}$

${(\frac{3}{4})}^{231} \cdot {(\frac{4}{9})}^{230} \cdot 3^{233}$

$\frac{7^{102}}{{(49^{10})}^{5}}$

${(\frac{4}{9} \cdot \sqrt[3]{64})}^{\frac{1}{2}}$

Exercise 2

Write the following powers of $x$ without negative and/or rational exponents.

$x^{-1}$

$x^{- \frac{1}{2}}$

$x^{\frac{3}{4}}$

$x^{1 \frac{3}{4}}$

$3 x^{-1,5}$

$\frac{1}{2} x^{-2,75}$

Exercise 3

Write as a power of $x$ :

$\frac{1}{x^{2} \sqrt{x}}$

$\frac{1}{3 \cdot \sqrt[4]{x}}$

$\frac{1}{2} \sqrt{x}$

$\frac{1}{2 x \sqrt{x}}$

${(3 x \sqrt{x})}^{3}$

Exercise 4

Compute the exact answer step by step without using the calculator. Show how you use the rules for powers.

${(2^{3})}^{2}$

$2^{3} \cdot 2^{2}$

${(2^{\frac{1}{4}})}^{8}$

$1000^{\frac{1}{3}}$

$\sqrt[3]{1000}$

$7^{\frac{1}{4}} \cdot 7^{\frac{3}{4}}$

$625^{\frac{1}{4}}$

$4^{2 \frac{1}{2}}$

Exercise 5

You can use the computational rules to rewrite certain expressions in $x$ into a power of $x$ . The end result is shown. Add the steps that were not shown.

${(2 x^{3})}^{4} \cdot -3 x^{5} = -48 x^{17}$

$\frac{2 x \cdot x^{2}}{x^{4}} = 2 x^{-1}$

$4 x^{2} \cdot \sqrt[3]{x} = 4 x^{2 \frac{1}{3}}$

$\frac{2}{x \sqrt{x}} = 2 x^{-1 \frac{1}{2}}$

$\frac{1}{2} x^{-1 \frac{1}{3}} = \frac{1}{2 x \sqrt[3]{x}}$

$\frac{{(2 \sqrt{x})}^{3}}{x^{2} \sqrt[3]{8 x}} = x^{- \frac{5}{6}}$

Exercise 6

Write the following functions as $f (x) = b \cdot g^{x}$ .

$f (x) = 3 \cdot 2^{0,5 x}$

$f (x) = 0, 5^{- x + 2}$

$f (x) = 9 \cdot {(\frac{1}{3})}^{4 - 2 x}$

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