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Number Systems

Short Answer Type

151. Simplify

fourth root of straight x to the power of bevelled 2 over 3 end exponent end root

and express the result in the exponential form of x.

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152. Find the value of ‘p’ if 5^p-3 × 3^{2p - 8} = 225.

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153. Simplify:

open parentheses 81 over 16 close parentheses to the power of negative begin inline style 3 over 4 end style end exponent cross times open parentheses 25 over 9 close parentheses to the power of negative 3 over 2 end exponent

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154.
If a = 2, b = 3, then find the values of the following:

(i) (a^b + b^a)^-1 (ii) (a^a + b^b)^-1

(i) (a^b+b^a)^-1

= (2³+ 3²)^-1
= (8 + 9)^-1
= (17)^-1

= $1 over 17$

(ii) (a^a + b^b)

= (2² + 3³)^-1

= (4 + 27)^-1

= (31)^-1 $equals space 1 over 31$

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155.

Prove that $fraction numerator 2 to the power of 30 plus 2 to the power of 29 plus 2 to the power of 28 over denominator 2 to the power of 31 plus 2 to the power of 30 minus 2 to the power of 29 end fraction equals 7 over 10$