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Oduvanchick [21]
3 years ago
9

Simplify 7^-5/6*7^-7/6

Mathematics
1 answer:
DochEvi [55]3 years ago
3 0

So the rule with multiplying exponents of the same base is x^m*x^n=x^{m+n} . Apply this rule here:

7^{-\frac{5}{6}}*7^{-\frac{7}{6}}=7^{-\frac{5}{6}+{-\frac{7}{6}}}=7^{-\frac{12}{6}}=7^{-2}

Next, the rule with converting negative exponents into positive ones is x^{-m}=\frac{1}{x^m} . Apply this rule here:

7^{-2}=\frac{1}{7^2}=\frac{1}{49}

<u>Your final answer is 1/49.</u>

<h2>------------------------------------------------</h2>

So an additional rule when it comes to exponents is x^{\frac{m}{n}}=\sqrt[n]{x^m}

In this case, your fractional exponent, x^9/7, would be converted to \sqrt[7]{x^9} . However, I had just realized you can further expand this.

Remember the rule I had mentioned earlier about multiplying exponents of the same base? Well, you can apply it here:

\sqrt[7]{x^9}=\sqrt[7]{x^7*x^2}=x\sqrt[7]{x^2}

Your final answer would be x\sqrt[7]{x^2}

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