Q. 34.2( 13 Votes )

# Which is larger: (5^{3} × 5^{4} × 5^{5} × 5^{6}) or (5^{7} × 5^{8})?

Answer :

5^{3} × 5^{4} × 5^{5} × 5^{6} = 5^{(3 + 4 + 5 + 6)}

⇒ 5^{3} × 5^{4} × 5^{5} × 5^{6} = 5^{18}

5^{7} × 5^{8} = 5^{(7 + 8)}

⇒ 5^{7} × 5^{8} = 5^{15}

Since the power of 5 in 5^{3} × 5^{4} × 5^{5} × 5^{6} is greater so 5^{3} × 5^{4} × 5^{5} × 5^{6} is greater than 5^{7} × 5^{8}

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The number of pairs positive integers (m,n)such that m^{n} =25 is

Simplify:

3^{1} × 3^{2} × 3^{3} × 3^{4} × 3^{5} × 3^{6} .

If (2^{m})^{4} = 4^{6}, find the value of m.

Use the laws of exponents and simplify.

Karnataka Board - Mathematics Part II

Can you find two integers m,n such that 2^{m + n} = 2^{mn} ?

Suppose m and n are distinct integers. Can be an integer? Give reasons.

Karnataka Board - Mathematics Part IISimplify:

Karnataka Board - Mathematics Part II

Suppose b is a positive integer such that is also an integer. What are the possible values of b?

Karnataka Board - Mathematics Part IIWhich is larger: (5^{3} × 5^{4} × 5^{5} × 5^{6}) or (5^{7} × 5^{8})?

Simplify:

2^{2} × 3^{3} × 2^{4} × 3^{5} × 3^{6}.