Solve (10×7×9)^(-5): Negative Exponent Expression Challenge

Insert the corresponding expression:

(10×7×9)−5= \left(10\times7\times9\right)^{-5}=

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Step-by-step video solution

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00:00 Simplify the following problem
00:03 According to the exponent laws, when we have a negative exponent
00:06 We can convert to the reciprocal number and obtain a positive exponent
00:09 We will apply this formula to our exercise
00:12 We'll write the reciprocal number (1 divided by the number)
00:17 Proceed to raise it to the positive exponent
00:23 This is the solution

Step-by-step written solution

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1

Understand the problem

Insert the corresponding expression:

(10×7×9)−5= \left(10\times7\times9\right)^{-5}=

2

Step-by-step solution

We have the expression (10×7×9)−5\left(10 \times 7 \times 9\right)^{-5}.

According to the rule for negative exponents, which states that a−n=1ana^{-n} = \frac{1}{a^n}, this expression can be rewritten as the reciprocal:

(10×7×9)−5=1(10×7×9)5\left(10 \times 7 \times 9\right)^{-5} = \frac{1}{\left(10 \times 7 \times 9\right)^5}.

Thus, the simplified expression is:

1(10×7×9)5\frac{1}{\left(10 \times 7 \times 9\right)^5}.

3

Final Answer

1(10×7×9)5 \frac{1}{\left(10\times7\times9\right)^5}

Practice Quiz

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\( 112^0=\text{?} \)

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