The value of the expression is 0.0265. Using exponents and power rules, the required value is calculated.
What are the exponent and power rules?
The important exponent and power rules are:
- a⁻ⁿ = 1/aⁿ; negative exponent
- (ab)ⁿ = aⁿ × bⁿ; power of a product rule
- aⁿ × aˣ = aⁿ⁺ˣ; multiplication rule
- aⁿ/aˣ = aⁿ⁻ˣ; division rule
- [tex]a^{\frac{x}{y} } = \sqrt[y]{a^x}[/tex]; fractional exponent
Calculation:
The given expression is [tex]126^{-3/4}[/tex]
Using calculator: [tex]126^{-3/4}[/tex] = 0.0265
Applying the exponent rule for evaluating the given expression:
[tex]126^{-3/4}[/tex]
Applying the negative power rule;
I.e., a⁻ⁿ = 1/aⁿ
⇒ [tex]126^{-3/4}=\frac{1}{126^{3/4}}[/tex]
Applying fractional exponent rule;
I.e., [tex]a^{\frac{x}{y} } = \sqrt[y]{a^x}[/tex]
⇒ [tex]\frac{1}{126^{3/4}}=\frac{1}{\sqrt[4]{126^3} }[/tex]
⇒ 1/[tex]\sqrt[4]{2000376}[/tex]
⇒ 1/37.6077
⇒ 0.0265
Therefore, the value of the given expression is 0.0265.
Learn more about exponent rules here:
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