Video: Evaluating Numerical Expressions with Integer Exponents Using Laws of Exponents

Calculate 4⁴ × 4.

03:27

Video Transcript

Calculate four to the power of four multiplied by four.

Before answering this question, it is worth remembering one of our laws of exponents, or indices. 𝑎 to the power of 𝑥 multiplied by 𝑎 to the power of 𝑦 is equal to 𝑎 to the power of 𝑥 plus 𝑦. When we are multiplying the same number raised to two different powers, we can add the powers, or exponents.

The number four is the same as four to the power of one. We can therefore rewrite four to the power of four multiplied by four as four to the power of four plus one. Four plus one is equal to five. So, our calculation simplifies to four to the power of five. We can type this into the calculator using the button 𝑥 with a little square above it. This means 𝑥 raised to a power.

We type four, the power or exponent button, then five. This will show up on our calculator display as four to the power of five. We then press equals to obtain our answer. Four to the power of five is equal to 1024. This means that four to the power of four multiplied by four is also 1024.

If we didn’t have a calculator, we can work out four to the power of five by multiplying four by itself five times. We multiply four by four by four by four and by four. Four multiplied by four is equal to 16. We could multiply this by four, or we could group two of the other fours. This simplifies the calculation to 16 multiplied by 16 multiplied by four.

We can calculate 16 multiplied by 16 using the grid method. We firstly split both of the 16s into 10 and six. 10 multiplied by 10 is 100. Six multiplied by 10 and 10 multiplied by six are both equal to 60. Six multiplied by six is equal to 36. Adding 100, 60, 60, and 36 gives us 256. Therefore, 16 multiplied by 16 is 256.

Our final step is to multiply this by four. 200 multiplied by four is equal to 800. 50 multiplied by four is equal to 200. Six multiplied by four is equal to 24. Adding these three numbers gives us 1024. Therefore, 256 multiplied by four is 1024. This proves that the answer we got on our calculator is correct.

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