Exponents: Number Sense Activities -

These should be approached without a calculator. A calculator might be used to check solution.

Number Sense Activity 1:

Compare the first five powers of 4 with the first ten powers of 2. Explain the pattern. Choose various values of $m$ and $n$ such that the following equation is true:

$2^m=4^n$

Number Sense Activity 2:

Write three different equations, choosing values for $m$ and $n$ carefully such that the equation

$3^m=9^n$

is true. Check your equations with a calculator.

Number Sense Activity 3:

Which one of the following is true:

$\frac{4^6}{5^6}&\geq \frac{4^7}{5^7}$

$\frac{4^6}{5^6}&= \frac{4^7}{5^7}$

$\frac{4^6}{5^6}&\leq \frac{4^7}{5^7}?$

Number Sense Activity 4:

Which is bigger;

$\frac{2^6}{3^7}$

$\frac{2^7}{3^6}?$

Number Sense Activity 5

Put the values in the correct place in the table

$\boxed{\frac{2^3}{3^3};\quad \frac{2^5}{2^{10}}; \quad \frac{10^6}{10^7}; \quad \frac{8}{1.9^3}; \quad \frac{3.2^3}{27} }$

Ball park	Value
Between 0 and 0.5
Between 0.5 and 1
More than 1	.

Number Sense Activity 6:

Which is bigger,

$1 \times 2 \times 3 \times 4 \times 5 \times 6$

$2^8$ ?

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