Simplifying (7^5)^3 as power of 7: Would it just be 7^8?

[Jagjit]

I have been doing these gcse practice examination papers, and one of the questions was,

Simplify fully (7[sup:30fbfsbr]5[/sup:30fbfsbr])[sup:30fbfsbr]3[/sup:30fbfsbr]
Give your answer as a power of 7.

Anyone help? Would it just be 7[sup:30fbfsbr]8[/sup:30fbfsbr]

Thank you.

 

[royhaas]

Write 7^5 three times, then multiply.

 

[Deleted member 4993]

I have been doing these gcse practice examination papers, and one of the questions was,

Simplify fully (7[sup:zhcy297f]5[/sup:zhcy297f])[sup:zhcy297f]3[/sup:zhcy297f]
Give your answer as a power of 7.

Anyone help? Would it just be 7[sup:zhcy297f]8[/sup:zhcy297f]

Thank you.

\(\displaystyle (a^m)^n\, =\, a^m\cdot a^m\cdot a^m\cdot a^m\cdot a^m\,...\, \cdot a^m\cdot a^m \, = \, a^{m+m+m....+m+m} \, = \, a^{(m\cdot n)}\)

 

[sgtpepper]

Yes, it would be 7^8. But you can still simplify further since neither 7 nor 8 are variables. Your actual simplified answer would be:

7 * 7 * 7 * 7 * 7 * 7 * 7 * 7 = 7^8 = 5,764,801


http://tinyurl.com/5lqz24

 

[masters]

As stated in Subhotosh Khan's post:

\(\displaystyle (7^5)^3=7^{15}\)

Since he stated the rule as: \(\displaystyle (a^m)^n=a^{mn}\)

Be careful not to confuse that with this:

\(\displaystyle a^m \cdot a^n=a^{m+n}\)

Had the original expression been \(\displaystyle 7^5 \cdot 7^3\)

Then, the answer would've been \(\displaystyle 7^8\)

But, that was not what was presented originally.

 

[sgtpepper]

Sorry! I don't know what I was thinking, or not thinking I guess...

 

[stapel]

Your actual simplified answer would be....5,764,801

Sorry, but no: the expression for the answer is required to be in the form "seven to some power".

Eliz.

 

[Denis]

Sorry! I don't know what I was thinking, or not thinking I guess...

This will be duly noted on your file flap, and taken into consideration at your next annual performance review