Question Video: Simplifying Algebraic Expressions Using Laws of Exponents Mathematics

Video Transcript

Simplify 𝑥 to the power of five 𝑦 to the power of four over four multiplied by negative eight 𝑥 cubed 𝑦 to the power of five over five.

In order to multiply any two fractions, we simply multiply the two numerators and then, separately, the two denominators. 𝑎 over 𝑏 multiplied by 𝑐 over 𝑑 is equal to 𝑎𝑐 over 𝑏𝑑. Before multiplying fractions, it is always worth checking to see if we can cross simplify or cross cancel first.

Four and negative eight are both divisible by four, as four divided by four is one and negative eight divided by four is negative two. We therefore need to multiply 𝑥 to the power of five 𝑦 to the power of four by negative two 𝑥 cubed 𝑦 to the power of five over five.

In order to simplify this expression, we need to recall one of our laws of exponents or indices, 𝑥 to the power of 𝑎 multiplied by 𝑥 to the power of 𝑏 is equal to 𝑥 to the power of 𝑎 plus 𝑏. When multiplying, we need to add the powers or exponents. Let’s consider the 𝑥 terms first.

𝑥 to the power of five multiplied by 𝑥 cubed, or 𝑥 to the power of three, is equal to 𝑥 to the power of eight, as five plus three equals eight. 𝑦 to the power of four multiplied by 𝑦 to the power of five is equal to 𝑦 to the power of nine, as four plus five equals nine.

As the only constant terms, a negative two on the top and five on the bottom, they stay as they are. The answer is negative two 𝑥 to the power of eight 𝑦 to the power of nine over five. This could also be written as negative two-fifths 𝑥 to the power of eight 𝑦 to the power of nine.