**HP 41/DM41L and TI-60X: Exponentiation of Large Numbers**

**But Why a Program when we have Button?**

This is true. What this program does is allow for calculation of y^x when results in answers greater than 9.999999999 * 10^9. The number is broken up into the form:

mantissa * 10^exponent

Let n = y^x. Then:

n = y^x

Taking the logarithm of both sides:

log n = log (y^x)

log n = x log y

A number can be split into its fractional and integer part:

log n = frac(x log y) + int(x log y)

Take the antilog of both sides:

n = 10^( frac(x log y) + int(x log y) )

n = 10^( frac(x log y) ) * 10^( int(x log y) )

where

mantissa = 10^( frac(x log y) )

exponent = int(x log y)

**HP 41/DM 41L Program BIGPOW**

Input:

Y stack: y

X stack: x

Output:

Y: mantissa (shown first)

X: exponent

01 LBL T^BIGPOW

02 X<>Y

03 LOG

04 *

05 ENTER↑

06 FRC

07 10↑X

08 STOP

09 X<>Y

10 INT

11 RTN

**TI-60 Program: Big Powers**

Input:

Store y in R1 and x in R2

Output:

R1 = mantissa (shown first), R2 = exponent

(Step, Key Number, Key)

00, 71, RCL

01, 02, 2

02, 65, *

03, 71, RCL

04, 01, 1

05, 43, log

06, 95, =

07, 61, STO

08, 02, 2

09, 78, Frac

10, 12, INV

11, 43, log

12, 61, STO

13, 01, 1

14, 13, R/S

15, 71, RCL

16, 02, 2

17, 79, Intg

18, 13, R/S

19, 22, RST

**Examples**

Example 1: 25^76. y = 25, x = 76

Result:

Mantissa = 1.75162308

Exponent = 106

25^76 ≈ 1.75162308 * 10^106

Example 2: 78^55.25, y = 78, x = 55.25

Result:

Mantissa = 3.453240284

Exponent = 104

78^55.25 ≈ 3.543240284 * 10^104

Eddie

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