Question

What is 6 to the power of -6 divided by 6 to the power of 7?

Answer 1

Hint: First we need to convert the given word problem into algebraic expression. That is, an algebraic expression in mathematics is an expression which is made up of variables and constants along with algebraic operations. An expression is a group of terms. Here algebraic operations are addition, subtraction, division and multiplication etc. After obtaining the algebraic expression we can simplify.

Complete step by step solution:
We have 6 to the power of -6 divided by 6 to the power of 7.
Now we know 6 to the power of 7 means \[ {6^7}\].
Now 6 to the power of -6 means \[ {6^{ - 6}}\]
Finally 6 to the power of -6 divided by 6 to the power of 7 means \[ \dfrac{{{6^{ - 6}}}}{{{6^7}}}\]
We need to solve this
\[ \Rightarrow \dfrac{{{6^{ - 6}}}}{{{6^7}}} = \dfrac{1}{{{6^{7 + 6}}}}\]
\[ \Rightarrow \dfrac{{{6^{ - 6}}}}{{{6^7}}} = \dfrac{1}{{{6^{13}}}}\]
Or
\[ \Rightarrow \dfrac{{{6^{ - 6}}}}{{{6^7}}} = {6^{ - 13}}\]
This is the required answer.
So, the correct answer is “\[ \dfrac{{{6^{ - 6}}}}{{{6^7}}} = {6^{ - 13}}\]”.

Note: Algebra helps in converting a mathematical statement into an equation. We know if we have ‘more’ or ‘sum’ in the given sentence we use the addition operation\[( + )\]. Similarly If we have ‘less’ or ‘difference’ we use subtraction \[( - )\]. If we have ‘quotient’ we use division operation \[( \div )\]. To define more generalized terms; we use algebra. It is a very vast branch of mathematics and is used in all the branches of mathematics like polynomial, linear equations, graphs, etc. and in daily life too.