Answer:
[tex]8^6[/tex]
Step-by-step explanation:
Powers are defined as the number of times you multiply a number by itself. For example, 2 to the 3rd power is 2 multiplied by itself 3 times. 2 * 2 * 2 = 8. You also know that if you multiply two powers of the same base, you add the exponent, and if you raise a power to a different power, you multiply the exponents.
e.g:
[tex]2^2\cdot2^2=2^{2+2}=2^4\\(2^2)^3=2^{2\cdot3}=2^6[/tex]
Now, we are asking to use grouping to write 2 to the power 18 as a power of 8. We know 2 to the power 8 is 2 to the power 3, so we have the following equation:
[tex]2^{18}=(2^3)^x[/tex]
We know this is now 2 to the power 3x = 2 the power 18, and therefore x = 6, because 3 times 6 is equal to 18. Now, we can just simplify 2 to the third as 8 and we now have:
[tex]8^6[/tex]
