#
Fast exponentiation
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Design a procedure
`solution`

that evolves an iterative exponentiation process that uses successive squaring and uses a logarithmic number of steps, as does
`fast-expt`

. (Hint: Using the observation that
`(bⁿ୵²)² = (b²)ⁿ୵²`

, keep, along with the exponent
`n`

and the base
`b`

, an additional state variable
`a`

, and define the state transformation in such a way that the product
`abⁿ`

is unchanged from state to state. At the beginning of the process
`a`

is taken to be 1, and the answer is given by the value of
`a`

at the end of the process. In general, the technique of defining an invariant quantity that remains unchanged from state to state is a powerful way to think about the design of iterative algorithms.)