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Question Video: Simplifying an Expression Using the Laws of Exponents Mathematics • 9th Grade

Simplify the expression (2π‘₯^(1/5)𝑦^(1/7))Β².

02:45

Video Transcript

Simplify the expression two π‘₯ to the power of one-fifth 𝑦 to the power of one-seventh all squared.

There are a couple of ways of approaching this problem. One way would be to recall that when we square a term, we multiply it by itself. This means that we could rewrite the expression as two π‘₯ to the power of one-fifth 𝑦 to the power of one-seventh multiplied by two π‘₯ to the power of one-fifth 𝑦 to the power of one-seventh. We could then use one of our laws of exponents or indices to simplify this expression. We know that π‘Ž to the power of π‘₯ multiplied by π‘Ž to the power of 𝑦 is equal to π‘Ž to the power of π‘₯ plus 𝑦. When multiplying terms with the same base, we simply add the exponents. Two multiplied by two is equal to four.

Next, we need to multiply π‘₯ to the power of one-fifth by π‘₯ to the power of one-fifth. As one-fifth plus one-fifth is equal to two-fifths, this is equal to π‘₯ to the power of two-fifths. We repeat this with the 𝑦-parts of our expression. One-seventh plus one-seventh is equal to two-sevenths, giving us 𝑦 to the power of two-sevenths. The simplified version of our expression is therefore equal to four π‘₯ to the power of two-fifths 𝑦 to the power of two-sevenths.

An alternative method would be to rewrite the expression by squaring each of the individual parts. This would give us two squared multiplied by π‘₯ to the power of one-fifth squared multiplied by 𝑦 to the power of one-seventh squared. We can then use the fact that π‘Ž to the power of π‘₯ all raised to the power of 𝑦 is equal to π‘Ž to the power of π‘₯ multiplied by 𝑦. We begin by calculating two squared which is equal to four.

Next, we need to multiply the exponents one-fifth and two. This is equal to two-fifths. So we have π‘₯ to the power of two-fifths. One-seventh multiplied by two is equal to two-sevenths, giving us 𝑦 to the power of two-sevenths. This confirms that the expression two π‘₯ to the power of one-fifth 𝑦 to the power of one-seventh squared is equal to four π‘₯ to the power of two-fifths 𝑦 to the power of two-sevenths.

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