Video Transcript
Find the quotient 21 𝑎 to the power of six 𝑏 divided by seven 𝑎𝑏.
In order to answer this question, we need to consider one of the laws of indices: 𝑥 to the power of 𝑝 divided by 𝑥 to the power of 𝑞 is equal to 𝑥 to the power of 𝑝 minus 𝑞. When we are dividing, we need to subtract the exponents or indices.
Let’s consider 21 𝑎 to the power of six 𝑏 or 𝑏 to the power of one divided by seven 𝑎𝑏. Well, 21 divided by seven is equal to three. 𝑎 to the power of six divided by 𝑎 is 𝑎 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 𝑎 to the power of five. 21 𝑎 to the power of six 𝑏 divided by seven 𝑎𝑏 is three 𝑎 to the power of five.
