# equality with integer exponents

n = var("n",domain = ZZ) assume(n>0) bool(3^(2*n) == (3^2)^n )

reply: False

Why?

Big thangs

equality with integer exponents

n = var("n",domain = ZZ) assume(n>0) bool(3^(2*n) == (3^2)^n )

reply: False

Why?

Big thangs

add a comment

0

When asked for a Boolean expression, SageMath returns `False`

if it is not capable to evaluate the expression to either true or false (a real false). This is what is happening in the present case; SageMath does not detect the identity:

```
sage: (3^(2*n) - (3^2)^n).simplify_full()
-9^n + 3^(2*n)
```

SymPy is more clever:

```
sage: (3^(2*n) - (3^2)^n)._sympy_().simplify()
0
```

Well, SageMath can get it with `canonicalize_radical()`

:

```
sage: (3^(2*n) - (3^2)^n).canonicalize_radical()
0
```

Asked: **
2019-12-23 10:22:48 -0600
**

Seen: **40 times**

Last updated: **Dec 23 '19**

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