Video: Simplifying Algebraic Fractions

Find the quotient 21π‘ŽβΆπ‘/7π‘Žπ‘.

01:13

Video Transcript

Find the quotient 21 π‘Ž to the power of six 𝑏 divided by seven π‘Žπ‘.

In order to answer this question, we need to consider one of the laws of indices: π‘₯ to the power of 𝑝 divided by π‘₯ to the power of π‘ž is equal to π‘₯ to the power of 𝑝 minus π‘ž. When we are dividing, we need to subtract the exponents or indices.

Let’s consider 21 π‘Ž to the power of six 𝑏 or 𝑏 to the power of one divided by seven π‘Žπ‘. Well, 21 divided by seven is equal to three. π‘Ž to the power of six divided by π‘Ž is π‘Ž to the power of five as six minus one is five. And 𝑏 divided by 𝑏 is 𝑏 to the power of zero as one minus one is zero.

As we know that anything to the power of zero is equal to one, the answer is three π‘Ž to the power of five. 21 π‘Ž to the power of six 𝑏 divided by seven π‘Žπ‘ is three π‘Ž to the power of five.

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