Easy

# Exponents and Radicals: Problems with Solutions

Problem 1
Which of the following is true?
Problem 2
Which of the following is true?
Problem 3
Which of the following is true?
Problem 4
Which property is used?
$3^{5} \cdot 3^{2}\cdot 3^{-3}=3^{4}$

Problem 5
Which property is used?

$\frac{2^{12}}{2^{8}}=16$

Problem 6
Which property is used?
$(2^{2})^{3}=64$

Problem 7
Which property is used?
$\left( \frac{5}{2}\right) ^{3}=\frac{125}{8}$

Problem 8
$5^{2}\cdot 5^{3}=$
Problem 9
Which property is used?
$(2\times 3)^{3}=216$

Problem 10
Find the value of x if
$3^{10}=3^{6}\cdot 3^{x}$

Problem 11
$a^{0}\cdot a^{8}=$
Problem 12
$(a^{5})^{6}=$
Problem 13
Find the value of n.
$(3^{2})^{3}=n^{6}$
Problem 14
$\frac{4^{8}}{4^{4}}=$
Problem 15
$\frac{a\cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a}{a \cdot a}=$
Problem 16
$\frac{5^{6}}{5^{-1}}=$
Problem 17
$\frac{x^{12}}{x^{6}}=$
Problem 18
Find The value of x.
$\frac{9^{x}}{9^{2}}=9^{5}$
Problem 19
$(2x^{3})^{4}=$
Problem 20
$(\frac{z^{2}}{2})^{3}=$
Problem 21
$(2\cdot y^{4})^{3}=$
Problem 22
$x^{1+\frac{5}{3}}=$
Problem 23
$\left( \sqrt[3]{x}\right)^{2}=$
Problem 24
$x^{1-\frac{3}{2}+\frac{5}{4}} =$
Problem 25
$\left( \sqrt{\sqrt[3]{x}}\right)^{5}=$
Problem 26
What is the result of $\left( \frac{x^{2}}{2y}\right)^{3}-\left( \frac{x^{2}}{y^{3}}\right)$ ?
Problem 27
What is the result of $\left( \frac{x^{2}}{2y}\div \frac{2y^{2}}{3x}\right)^{2}$ ?
Problem 28
What is the result of $\left(\frac{ab}{2c}\right)^{3}\div \left( \frac{a.b}{c^{3}}\right)^{2}$ ?
Problem 29
Evaluate the expression $5^{x}-3^{x}$ when $x=3$.
Problem 30
What is the value of n if $3^{n}=3^{2}\cdot 3^{3}$
Problem 31
What is the value of n if $8^{n}=2^{-2} \cdot 4^{3}$?
Problem 32
What is the value of $x$ if $2^{2x-1}=4$
Problem 33
What is the value of $n$ if $27^{n}=3^{2}\cdot 9^{3}$
Problem 34
What is the value of $x$ if
$\sqrt[3]{8^{x}}=128$
Easy

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