Applying Combined Exponents Rules: Variable in the exponent of the power

Factoring Out the Greatest Common Factor (GCF)More than one unknownWorded problemsUsing variablesComplete the equationUsing laws of exponents with parametersFactorizationMultiplying Exponents with the same baseTrinomialconverting Negative Exponents to Positive ExponentsNumber of termsPresenting powers with negative exponents as fractionsTwo VariablesIdentify the greater valuePresenting powers in the denominator as powers with negative exponentsBinomialVariables in the exponent of the powerSingle VariableUsing the laws of exponentsVariable in the base of the powerPresenting powers with negative exponents as fractionsApplying the formulaCalculating powers with negative exponentsMonomialA power lawUsing multiple rules
Question 1

\( x^{-a}=\text{?} \)

Question 2

\( 8^{-2x}=\text{?} \)

Question 3

Simplify the following:

\( \frac{a^{20b}}{a^{15b}}\times\frac{a^{3b}}{a^{2b}}= \)

Question 4

\( (g\times a\times x)^4+(4^a)^x= \)

Examples with solutions for Applying Combined Exponents Rules: Variable in the exponent of the power

Exercise #1

x−a=? x^{-a}=\text{?}

Video Solution

Step-by-Step Solution

We use the exponential property of a negative exponent:

b−n=1bn b^{-n}=\frac{1}{b^n} We apply it to the problem:

x−a=1xa x^{-a}=\frac{1}{x^a} Therefore, the correct answer is option C.

Answer

1xa \frac{1}{x^a}

Exercise #2

8−2x=? 8^{-2x}=\text{?}

Video Solution

Answer

164x \frac{1}{64^x}

Exercise #3

Simplify the following:

a20ba15b×a3ba2b= \frac{a^{20b}}{a^{15b}}\times\frac{a^{3b}}{a^{2b}}=

Video Solution

Answer

a6b a^{6b}

Exercise #4

(g×a×x)4+(4a)x= (g\times a\times x)^4+(4^a)^x=

Video Solution

Answer

g4a4x4+4ax g^4a^4x^4+4^{ax}