Video: Using Laws of Exponents to Evaluate Numerical Expressions

Calculate [(1/2)⁹ ÷ (1/2)³] ÷ (1/2)⁴.

01:08

Video Transcript

Calculate one-half to the ninth power divided by one-half to the third power, all divided by one-half to the fourth power.

To begin, we need to work within the brackets first. And notice that we’re dividing two fractions to powers. And the fractions are exactly the same, and here as well. So we’re working with like bases. And when dividing with like bases, we can actually subtract their exponents.

So we have one-half to the nine minus three power. And nine minus three is six. So we have one-half to the sixth power divided by one-half to the fourth power. So we have like bases again. And we’re dividing. So we can subtract our exponents. And six minus four is two. So to simplify, we need to take one to the second power on the numerator and take two to the second power on the denominator. One squared is one. And two squared is four. Therefore, our final answer will be one-fourth.

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